BEGIN:VCALENDAR
VERSION:2.0
X-WR-CALNAME;VALUE=TEXT:Harvard Logic Colloquium: Joel Hamkins
PRODID:-//Harvard events data//EN
BEGIN:VEVENT
UID:event_928041_0
SUMMARY:Harvard Logic Colloquium: Joel Hamkins
DESCRIPTION:<p><strong>Joel Hamkins</strong> (City University of New York): <em>Recent Advances in Set-theoretic Geology</em></p><p>Set-theoretic geology is the study of the set-theoretic universe V in the context of all its ground models and those of its forcing extensions. For example, a bedrock of the universe is a minimal ground model of it and the mantle is the intersection of all grounds. In this talk, I shall explain some recent advances, including especially the breakthrough result of Toshimichi Usuba, who proved the strong downward directed grounds hypothesis: for any set-indexed family of grounds, there is a deeper common ground below them all. This settles a large number of formerly open questions in set-theoretic geology, while also leading to new questions. It follows, for example, that the mantle is a model of and provably the largest forcing-invariant definable class. Strong downward directedness has also led to an unexpected connection between large cardinals and forcing: if there is a hyper-huge cardinal <span style="font-family:Symbol;">k</span>, then the universe indeed has a bedrock and all grounds use only <span style="font-family:Symbol;">k</span>-small forcing.</p>
LOCATION:Logic Center, Room 420, 2 Arrow Street
STATUS:CONFIRMED
DTSTART:20161020T200000Z
DTEND:20161020T210000Z
END:VEVENT
END:VCALENDAR